⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠭⡝⢎⠧⡝⢦⢋⠎⡱⢌⠊⡑⠨⠀⣾⡽⣺⣟⣿⣻⠿⢿⠻⠛⡽⢳⡿⣛⡶⣉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⢊⠱⠘⠤⢉⠂⠡⢀⠂⠄⠁⠸⢥⢛⡵⣻⠾⣍⠏⡑⠊⡀⠢⢍⡽⣳⠵⣉⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⢁⠂⠠⠈⠀⠄⠀⡀⢀⠉⢆⡹⢜⣣⠟⡸⡌⠤⣁⠰⣡⣚⠼⣡⠛⡔⢊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡠⢄⢆⣐⠢⣌⠲⣄⢣⡈⠄⢂⠓⣈⠹⡔⣩⠓⣌⠣⡕⢊⢇⠣⡙⠌⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⢞⡱⣍⠮⣜⡳⣜⡳⢜⣣⢝⣄⠈⠒⡀⠣⠐⣁⠊⠄⢣⠈⡅⠊⠔⡁⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⢶⣩⣟⣮⢷⡭⣰⢨⢲⣋⡞⡷⣄⠁⠤⠁⠄⡈⠐⠠⠁⠄⡉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣝⣯⣿⢾⣽⣳⡻⣼⣋⡶⣹⢞⡽⣏⡷⣤⠈⠀⠠⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣹⢮⣟⣯⣞⡷⣯⢷⣛⡾⣽⢮⣓⢮⡓⢧⣋⠖⡠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣻⡟⣾⣳⢯⣿⣽⣻⢿⣽⣳⡟⣮⢧⡛⢦⢣⡙⠤⢃⠂⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⣿⢳⣭⢿⣾⣯⣿⡿⣟⣯⣟⣧⢷⣹⠣⢇⡜⢢⠁⠎⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢞⣯⡻⣎⡿⣽⣻⣽⣿⣻⡽⣞⢾⣹⡒⡏⢎⠬⡑⢌⠢⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣧⢿⡎⡽⣳⢯⣟⠷⣯⢟⡮⣳⢎⡵⡙⣌⠲⡁⢎⡐⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣞⣻⠦⠑⣯⣛⣮⢻⣥⣛⠶⣩⢎⡴⣑⠢⠥⡑⢢⢌⡑⢆⡘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣯⢿⣽⣛⠆⣳⡽⣎⢷⢞⡼⣫⢵⡚⡴⢣⣙⠲⡉⢖⢢⡙⢦⡙⣆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⡞⣿⢶⡽⣯⣷⣻⣞⡿⣎⡷⣽⡲⣝⢎⡳⢌⣣⡙⢬⠲⣭⢳⣙⠦⣉⠔⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢬⡹⣝⢾⡻⣷⢯⡟⣾⢽⣫⢗⣧⡛⣬⠣⣝⠢⡕⣌⠣⢏⠲⡭⢺⡱⢣⡚⡔⡡⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡝⡦⢱⢋⠾⣹⠺⣭⢻⡝⢮⢧⠻⣔⠫⢖⡹⢄⠫⠔⡌⠳⡌⠳⡍⢧⣛⡥⣻⡜⣱⣃⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣙⢲⡡⢎⠓⡥⡛⡴⢣⡝⡎⣎⠳⡌⠓⡌⡔⢌⢊⡱⢌⢣⠘⢥⡙⡲⣥⣛⢦⢿⡱⣞⣬⡓⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢍⠶⢱⢈⠓⠴⣁⢣⠣⠜⡘⠤⢓⠨⡑⠰⡈⢂⠒⡰⠈⠆⣉⠦⡑⢧⡚⣼⢫⡟⣵⢫⢶⣙⢖⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡿⡌⢎⡑⡊⢌⠒⡄⢢⢁⠣⡘⠌⠢⠡⠘⡐⠌⠄⠣⡐⣉⠒⡌⢢⡙⢦⣙⢮⡳⡽⣞⢯⣳⢎⡧⢽⡱
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢼⣱⣊⠠⡉⠆⡒⡈⢄⢂⠡⡐⠌⢡⢈⠡⠐⠌⡈⠔⡐⠤⠑⡌⢢⡑⢦⠩⣖⠽⡼⣹⢧⣛⠾⣌⢧⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡻⣤⡛⣤⡘⠤⢃⠸⡀⠄⢃⠠⢘⡀⢄⠸⠘⠄⢣⠘⢠⠃⢇⠸⢃⡸⢄⢻⡘⢧⢻⣇⣟⢿⡻⡜⣇⠿⣸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣝⣧⣛⢦⡝⢦⡁⢒⠡⢊⠤⢑⠢⡐⢂⠆⡩⠌⡂⠍⠤⡉⢆⡡⠣⣘⢬⣖⣾⣫⣟⡾⡼⣧⢏⠷⣩⠞⣡⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣻⣼⣫⠿⣼⢣⡝⣢⢁⠣⡘⢄⠣⣘⠐⡊⠥⡘⠤⡉⢆⠱⣢⡕⣾⣳⣛⡾⣎⢷⣫⢿⣱⣛⢮⡝⣥⢛⠴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⣱⢾⣭⡿⣭⡳⡝⣦⡓⡤⠑⢌⡱⢠⠋⡜⢠⠱⡘⢄⣡⣾⡱⣿⡵⢯⣻⣽⢯⡿⣽⡞⡷⢯⣞⡱⢎⢎⢒⠡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢲⣹⢮⡷⣻⡵⣹⣚⡴⣹⢒⡭⢠⠀⠁⠘⠀⠃⢂⣵⣫⣟⡶⣟⣧⣟⡿⣽⣺⢯⣷⢻⣞⡽⣳⢎⠵⣉⠆⠌⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⢮⣟⣷⢻⣵⢣⡟⡴⣋⠶⡡⣉⠂⠄⢀⠴⠿⠳⠻⠞⢿⡽⣳⢯⣟⢷⡯⣟⢾⡻⣜⠷⡹⢎⠲⠡⠌⡐⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣝⡾⡽⣞⣿⡼⣏⢾⡱⣍⠶⡑⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣭⢷⢯⢯⡗⣯⢫⡕⣋⠔⡡⠂⠄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢽⣹⠾⣽⡭⢷⡹⣌⠲⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⡯⣯⡝⣮⠓⡜⠠⠒⡀⢁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠻⠧⠛⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣛⢆⠫⢐⢁⠢⠐⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢊⠔⠂⠄⢂⠁⢀